10/2x=35/4x+33

Solution for 10/2x=35/4x+33 equation:

10/2x=35/4x+33

We move all terms to the left:

10/2x-(35/4x+33)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x+33)!=0

x∈R


We get rid of parentheses

10/2x-35/4x-33=0

We calculate fractions


40x/8x^2+(-70x)/8x^2-33=0

We multiply all the terms by the denominator


40x+(-70x)-33*8x^2=0

Wy multiply elements

-264x^2+40x+(-70x)=0

We get rid of parentheses

-264x^2+40x-70x=0

We add all the numbers together, and all the variables

-264x^2-30x=0

a = -264; b = -30; c = 0;
Δ = b2-4ac
Δ = -302-4·(-264)·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-30}{2*-264}=\frac{0}{-528}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+30}{2*-264}=\frac{60}{-528}
=-5/44
$